Slighly confused on this

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Thu Jun 23, 2011 10:44 am

How many guests were present at the party?
(1)There were 45 handshakes if the guests shook hands with each other and every two guests shook hands exactly once.
(2)if there were half as many guests present, they could sit in a row in 120 different ways.

(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Detailed explanations would be appreciated

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Source: Beat The GMAT — Data Sufficiency | Thu Jun 23, 2011 10:44 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jun 23, 2011 10:55 am

Hi,
From(1):
If there are n guests, then there will be nC2 pairs. As each pair contribute 1 hand shake, ther will be nC2 handshakes
So, nC2 = 45 => n=10
Sufficient
From(2):
x elements can be arranged in a row in x! ways.
(n/2) guests sit in a row in 120 ways i.e. 5!
So, n/2 = 5 =>n=10
Sufficient

Hence, D

Cheers!

Things are not what they appear to be... nor are they otherwise

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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 amFollowed by: 1 member; Thanked: 4 times; GMAT Score:700

by mirantdon » Mon Jun 27, 2011 11:21 am

confer with Frankenstein
IMO D

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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 amFollowed by: 1 member; Thanked: 4 times; GMAT Score:700

by mirantdon » Mon Jun 27, 2011 11:24 am

but is it nc2 . .
i think it should be ..
for n people, number of handshakes is 1+2+3...+ (n-1)
so this is arithmetic sequence so sum of it is number of handshakes
S= ((n-1)/2 * (1+ (n-1))
S= (n^2-n) / 2

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Tue Jun 28, 2011 11:44 pm

a n*(n-1)/2 = 45 thus n= 10 sufficient.

b (n/2)!= 120 means n/2=5 n=10. sufficient.

D it is.

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